CS 7960, Advanced Image ProcessingSpring 2010, Prof. Guido GerigProject 1: Scale-Space SelectionOut: Thursday Feb-11-2010Due: Thursday Feb-24-2010Office hours: Tue 1pm to 3pm, please contact me in advance or for other arrangements.Required Readings: Papers and Materials Anisotropic DiffusionAdditional information: “Medical Image Analysis” Notes West Virginia, CS 593 791, availableon WebCt and on my web-page under Lecture “Anisotropic Diffusion”1 Nonlinear scale space by anisotropic diffusionYou need to implement the anisotropic diffusion partial differential equation as a forward-in-time-centered-space (FTCS) discrete implementation. The implementation is in its spirit as youfind in the paper and as discussed in the class.Figure 1: Example of scale space representations from linear diffusion (top) and nonlineardiffusion (bottom).The filtering has two parameters, the time t which is proportional to the number of iterations,and the parameter κ of the conductivity function. Remember that the degree of smoothingis not linear with the time t, but logarithmic (see FEV Chapter 3 discussion 3.3 on cascadingproperty and 3.7 on binomial coefficients, i.e. if you see each step as a convolution you can geta feeling how the resulting variance and the standard deviation changes!).Remember our discussion that the value κ serves as an “edge threshold”, i.e. selecting edgestrengths that are preserved where others are blurred.A possible strategy for your program is outlined below:• Implement a numerical solution to the partial differential equation of the anisotropic dif-fusion.• Use the common conductivity function (Gaussian) as shown in the Perona and Malikpaper.• Similarly to Perona and Malik’s paper, best is not only to compare the resulting imagesbut the edge maps. Looking at your code, you see that at every iterations, you actuallycalculate the local gradient and can easily calculate the gradient magnitude. Your programcan output the images but also the gradient maps.• Read a test image, be creative about an image that would be interesting to smooth whilepreserving edges, which is an image that can be segmented by subdivision into homoge-neous patches.• Experiment with different κ-values and same number of time steps to observe differentlevels of details that are preserved or disappear, respectively. Show results with imagesand gradient maps.• Experiment with your choice of an interesting κ-value and different number of iterations,to observe the evolution of nonlinear scale space. Show results with images and gradientmaps. Remember that κ is related to the local gradients. Could you think about a conceptto automatically choose this parameter based on your image?• Remember that you can simulate linear scale-space by setting the κ-value very high, whichmeans much higher than the expected largest gradient maginitudes.• Compare the nonlinear scale space (with a few key images taken from the log-scaled numberof iterations) with linear scale space. Show results with images and gradient maps.• Discuss how such a nonlinear smoothing could help with the segmentation of one or few im-ages selected by you. E.g., how could you make use of the κ-value to select the componentsyou want to segment, and how could you make use of theYou should write up a report summarizing your procedure and discussing your results. Thereport should be written in html and accessible to the instructor via a web-browser.• Description of method to implement the PDE of the anisotropic diffusion.• Description of the conductivity function you choose.• Application to images that you select as images that might benefit from such a procedure.• Description and illustration of smoothing performance under different κ-values and itera-tion numbers, as detailed above.• Discussion of preservation of details, i.e. different κ-values selectively preserve differentdetails, which might be useful for specific segmentation task (like e.g. segmentation of textlines into words and then into characters, just as an analogy).• Discuss criteria mentioned in James Fishbaugh’s lecture as advantages and disadvantagesof linear versus nonlinear smoothing (blurring, edge sharpness, edge-dislocations, causality(no new structures created with scale), simplification of implementation and more.• Commentary about any issues that arose, ways for alternative implementations, potentialimprovements